LMFDB - Newform orbit 882.6.a.j

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,6,Mod(1,882)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("882.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	882.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$141.458529075$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$ q - 4 q^{2} + 16 q^{4} + 76 q^{5} - 64 q^{8}+O(q^{10}) $

$ q - 4 q^{2} + 16 q^{4} + 76 q^{5} - 64 q^{8} - 304 q^{10} - 650 q^{11} - 762 q^{13} + 256 q^{16} - 556 q^{17} + 2452 q^{19} + 1216 q^{20} + 2600 q^{22} + 2950 q^{23} + 2651 q^{25} + 3048 q^{26} + 674 q^{29} + 3024 q^{31} - 1024 q^{32} + 2224 q^{34} + 7730 q^{37} - 9808 q^{38} - 4864 q^{40} - 17016 q^{41} + 21836 q^{43} - 10400 q^{44} - 11800 q^{46} - 23940 q^{47} - 10604 q^{50} - 12192 q^{52} - 15594 q^{53} - 49400 q^{55} - 2696 q^{58} + 5608 q^{59} - 150 q^{61} - 12096 q^{62} + 4096 q^{64} - 57912 q^{65} - 43784 q^{67} - 8896 q^{68} + 39178 q^{71} + 23570 q^{73} - 30920 q^{74} + 39232 q^{76} - 17892 q^{79} + 19456 q^{80} + 68064 q^{82} + 38972 q^{83} - 42256 q^{85} - 87344 q^{86} + 41600 q^{88} + 6024 q^{89} + 47200 q^{92} + 95760 q^{94} + 186352 q^{95} - 108430 q^{97}+O(q^{100}) $

Display 100 coefficients 10 coefficients

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label

$\iota_m(\nu)$

$ a_{2} $

$ a_{3} $

$ a_{4} $

$ a_{5} $

$ a_{6} $

$ a_{7} $

$ a_{8} $

$ a_{9} $

$ a_{10} $

1.1

−4.00000

16.0000

76.0000

−64.0000

−304.000

Atkin-Lehner signs

$ p $	Sign
$2$	$1$
$3$	$-1$
$7$	$-1$

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	882.6.a.j		1
3.b	odd	2	1		294.6.a.k		1
7.b	odd	2	1		126.6.a.a		1
21.c	even	2	1		42.6.a.e	✓	1
21.g	even	6	2		294.6.e.d		2
21.h	odd	6	2		294.6.e.c		2
28.d	even	2	1		1008.6.a.d		1
84.h	odd	2	1		336.6.a.q		1
105.g	even	2	1		1050.6.a.f		1
105.k	odd	4	2		1050.6.g.h		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
42.6.a.e	✓	1	21.c	even	2	1
126.6.a.a		1	7.b	odd	2	1
294.6.a.k		1	3.b	odd	2	1
294.6.e.c		2	21.h	odd	6	2
294.6.e.d		2	21.g	even	6	2
336.6.a.q		1	84.h	odd	2	1
882.6.a.j		1	1.a	even	1	1	trivial
1008.6.a.d		1	28.d	even	2	1
1050.6.a.f		1	105.g	even	2	1
1050.6.g.h		2	105.k	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{6}^{\mathrm{new}}(\Gamma_0(882))$:

$ T_{5} - 76 $

$ T_{11} + 650 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 4 $ T + 4
$3$	$ T $ T
$5$	$ T - 76 $ T - 76
$7$	$ T $ T
$11$	$ T + 650 $ T + 650
$13$	$ T + 762 $ T + 762
$17$	$ T + 556 $ T + 556
$19$	$ T - 2452 $ T - 2452
$23$	$ T - 2950 $ T - 2950
$29$	$ T - 674 $ T - 674
$31$	$ T - 3024 $ T - 3024
$37$	$ T - 7730 $ T - 7730
$41$	$ T + 17016 $ T + 17016
$43$	$ T - 21836 $ T - 21836
$47$	$ T + 23940 $ T + 23940
$53$	$ T + 15594 $ T + 15594
$59$	$ T - 5608 $ T - 5608
$61$	$ T + 150 $ T + 150
$67$	$ T + 43784 $ T + 43784
$71$	$ T - 39178 $ T - 39178
$73$	$ T - 23570 $ T - 23570
$79$	$ T + 17892 $ T + 17892
$83$	$ T - 38972 $ T - 38972
$89$	$ T - 6024 $ T - 6024
$97$	$ T + 108430 $ T + 108430
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Overview	Random
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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	882.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
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